A nurse in the ward scolds John for his emotional display. What is she afraid will happen to the Bokanovsky group who are there for their death training?

To properly understand the nurse's reaction to John's emotional display, it is necessary to understand the social structure of the society presented in Brave New World. Compliant citizens are created through Bokanovsky's Process. This process forces fertilized eggs to split, creating a variety of clones or identical twins. Each group of Bokanovsky children is raised in isolation from their parents. The society in Brave New World does not believe in family structure, so these clones grow up with no concept of father or mother. Monogamous relationships are shunned in favor of romantic encounters devoid of commitment or attachment, so there is no reason for any citizens to grieve when another dies. They live in a community of individual isolation, a seemingly paradoxical existence that serves as the backdrop for the scene that takes place in the hospital in Chapter 14. The nurse is afraid that John's attachment to his mother, a normal social construct for the "Savages," will undermine the socially acceptable view on death.
When John cries and falls to his knees as his mother is dying, he is exhibiting what the nurse views as "anti-social" tendencies. The irony Huxley is trying to get across with this scene is that a natural reaction born of human social connections is viewed as being a danger to society. The twins are conditioned to view death as a regular part of life. Adult characters throughout the book exhibit this belief by flippantly acknowledging death and showing a lack of concern when other characters die. John is the only one who is remotely upset about his mother's impending death, and his reaction, as the nurse feared, leads to chaos in the emotionless society.
Even the Bokanovsky twins have the ability to feel fear, so exposure to someone who grieves the loss of another life is a threat to their conditioning. The nurse rightly assumes that their way of life can only exist in a carefully crafted environment in which all reactions are monitored and controlled. The children go on death tours to get them used to the idea of death before they are old enough to have an established concept of it as something negative. When they grow up, they are expected to view the deceased not as personal losses but as contributors to society in a different way. For example, Henry notes while flying over a crematorium that he is delighted that the dead are cremated and turned into something as useful to society as phosphorous.